Problem: Solve for $x$ and $y$ using elimination. ${x-4y = -13}$ ${-x+3y = 9}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x-4y = -13}\thinspace$ to find $x$ ${x - 4}{(4)}{= -13}$ $x-16 = -13$ $x-16{+16} = -13{+16}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {-x+3y = 9}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(4)}{= 9}$ ${x = 3}$